Problem: What do the following two equations represent? $2x-4y = 3$ $12x+6y = 2$
Solution: Putting the first equation in $y = mx + b$ form gives: $2x-4y = 3$ $-4y = -2x+3$ $y = \dfrac{1}{2}x - \dfrac{3}{4}$ Putting the second equation in $y = mx + b$ form gives: $12x+6y = 2$ $6y = -12x+2$ $y = -2x + \dfrac{1}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.